Accuracy in Recursive Minimal State Space Methods

We identify a critical condition, based on some qualitative properties of the expected marginal utility of consumption, that insure the accurate performance of frequently used methods in recursive macroeconomics. This condition can be found in a large fraction of applied papers. Moreover, in a model which does not satisfy the mentioned condition, we measure the bias of solutions using a closed form continuous recursive equilibrium. We found 2 sources of inaccuracy in minimal state space methods: the lack of a convergent operator and the inexistence of a well defined (stochastic) steady state. We found that a canonical procedure may sub-estimate (over-estimate) concentration (dispersion) measures with respect to the ergodic distribution of the model. It is shown that even a numerically convergent minimal state space (MSS) algorithm may not match the ergodic distribution of the model as the MSS equilibrium might not have a well defined steady state. These facts imply in turn that the computed effects of economic policies are also inacurate. Moreover, we identify a connection between the lack of convergence in the MSS algorithm and the equilibrium budget constraint which implies that simulated paths are distorted in any time period.